Q. would dearly love to know when Thayer's Lexicon was first published. Nowhere in my copy can I find this info.

The earliest edition of Thayer's Lexicon in this library's collection was published in 1887 --

Grimm, Carl Ludwig Wilibald, 1807-1891.
Lexicon Graeco-Latinum in libros Novi Testamenti. English A Greek-English lexicon of the New Testament : being Grimm's Wilke's Clavis Novi Testamenti / translated, revised and enlarged by Joseph Henry Thayer.
New York : Harper, 1887.
xix, 723 p. ; 27 cm.
Translation of:  Lexicon Graeco-Latinum in libros Novi Testamenti.
"List of ancient authors quoted or referred to": p. [xi]-xiv.
"List of books referred to": p. [xv]-xvii.

The title page verso indicates the book was copyrighted in 1886, and the preface is signed by the author in 1885.

I hope this information is useful.